Answer
$\log_{8}{\left(\frac{1}{4}\right)}=-\frac{2}{3}$
Work Step by Step
We are given:
$\frac{1}{4}=8^{-\frac{2}{3}}$
Recall the definition of a logarithm (pg. 451):
$\log_{b}{x}=y$ iff $b^y=x$
Applying this definition to our equation ($x=\frac{1}{4}, b=8, y=-\frac{2}{3}$), we get:
$\log_{8}{\left(\frac{1}{4}\right)}=-\frac{2}{3}$
